Material and texture for automatic faces

Hi,

if a mesh has only vertices and edges but no faces, i.e. no material can be assigned explicitly to faces, and the object has a screw modifier that creates the faces, which material is used for them? It seems to be the one in the first slot, but is this written anywhere?

And, how do you handle texture coordinates with such an object? In the node setup, I’ve tried the “generated” texture coordinate (and others) and also different rotations of the Mapping node, but nothing gives the intended result, i.e. I’d like to use a bump map for the faces. Do I have to do without the screw modifier in this case so that I’m able to assign UV coordinates?

EDIT:
Mesh in edit mode:

In object mode with screw modifier: